Let 
be a regular surface with 
points in the tangent
space 
of 
.
Then the third fundamental form is given by
 |
where 
is the shape operator.
Third Fundamental Form
See also
First Fundamental Form, Fundamental Forms, Second Fundamental Form, Shape OperatorExplore with Wolfram|Alpha
References
Gray, A. "The Three Fundamental Forms." §16.6 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 380-382, 1997.Referenced on Wolfram|Alpha
Third Fundamental FormCite this as:
Weisstein, Eric W. "Third Fundamental Form." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThirdFundamentalForm.html